for which the initial approximation \({\mathbf {\phi }}^0={\mathbf {0}}\)  can be conveniently used. It is also possible to use the simplified Newton iteration for solving (REF ) which, taking into account (REF ), (REF ), and that (see, e.g., [1]})
\({\cal P}_s^\top \Omega {\cal I}_s = X_s := \left(\begin{array}{cccc}\xi _0 &-\xi _1\\\xi _1 &0 &\ddots \\&\ddots &\ddots &-\xi _{s-1}\\& &\xi _{s-1} &0\end{array}\right), \qquad \xi _i = \left(2\sqrt{|4i^2-1|}\right)^{-1},\quad i=0,\dots ,s-1,~~\) 
